Question

Estimate the solution to the system of these linear equations based on the graph.

y=2x+3

y=12x+6

(1 point)

Ο (2,7)

Ο (2,-7)

Ο (7,2)

Ο (-2,7)

Answer 1

To solve the system of equations graphically, we want to find the point where the two lines intersect:

1. The first equation is \( y = 2x + 3 \).
2. The second equation is \( y = 12x + 6 \).

Let's find the point of intersection by equating the two equations:

\[
2x + 3 = 12x + 6
\]

Now, we can rearrange the equation:

\[
3 - 6 = 12x - 2x
\]
\[
-3 = 10x
\]

Dividing both sides by 10 gives:

\[
x = -\frac{3}{10}
\]

Now substitute \( x = -\frac{3}{10} \) into one of the equations to find \( y \). We'll use the first equation:

\[
y = 2\left(-\frac{3}{10}\right) + 3
\]
\[
y = -\frac{6}{10} + 3 = -\frac{6}{10} + \frac{30}{10} = \frac{24}{10} = \frac{12}{5}
\]

So, the point of intersection is:

\[
\left(-\frac{3}{10}, \frac{12}{5}\right)
\]

Now examining the choices provided:

- (2,7)
- (2,-7)
- (7,2)
- (-2,7)

None of these points match the point of intersection \((-0.3, 2.4)\). Therefore, we cannot confirm any of the given options as the solution based on the estimated graph intersection.

If you need further assistance or if there's something specific you would like to analyze or confirm from the options, please let me know!